TY - JOUR

T1 - QUANTUM KIRWAN MORPHISM AND GROMOV–WITTEN INVARIANTS OF QUOTIENTS III

AU - WOODWARD, C. H.R.I.S.T.

N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. We also give a formula for a solution to the quantum differential equation on X//G in terms of a localized gauged potential for X. These results overlap with those of Givental [14], Lian–Liu–Yau [21], Iritani [20], Coates–Corti–Iritani–Tseng [11], and Ciocan–Fontanine–Kim [7], [8].

AB - This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. We also give a formula for a solution to the quantum differential equation on X//G in terms of a localized gauged potential for X. These results overlap with those of Givental [14], Lian–Liu–Yau [21], Iritani [20], Coates–Corti–Iritani–Tseng [11], and Ciocan–Fontanine–Kim [7], [8].

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U2 - 10.1007/s00031-015-9336-7

DO - 10.1007/s00031-015-9336-7

M3 - Article

AN - SCOPUS:84945439812

VL - 20

SP - 1155

EP - 1193

JO - Transformation Groups

JF - Transformation Groups

SN - 1083-4362

IS - 4

ER -